Dynamic Transition Probabilities Research Articles

An epidemiological and economic simulation model to evaluate the spread and control of infectious bovine rhinotracheitis in the Netherlands

Bovine herpesvirus type I (BHV1), causing infectious bovine rhinotracheitis (IBR), was introduced in the Netherlands in 1971. In 1993, about 42% of the dairy cows had antibodies against BHV1. In the future, stricter requirements are anticipated regarding the health status of exported breeding cows and material. To support policymakers in their decisions on IBR eradication, a simulation model was developed in which the epidemiological and economic consequences of various control strategies were evaluated. This paper describes the model and provides an overview of some important outcomes. In the model, dairy herds were classified into different disease states based on (1) the reproduction ratio of the disease ( R, defined as the number of secondary cases caused by one infectious animal) (2) the within-herd prevalence, within each value of R and (3) the expected number of infectious animals in an infectious herd within each prevalence range. The dynamic transition probability of a herd going from one state to another per week depends on direct contacts between animals, and other contacts such as transmission through fomites, indirect transmission through other species, airborne transmission and minor disease-specific routes such as venereal or iatrogenic transmission. Five control strategies, including both a voluntary vaccination program and a compulsory vaccination program for all dairy herds were evaluated. A voluntary vaccination program with 50% participation is not expected to lead to eradication of IBR. It appears that compulsory vaccination would be necessary to reach an IBR-free status.

Nonstationary hidden Markov model

The standard hidden Markov model (HMM) has often been pointed out for its inappropriateness in capturing state duration behavior. Explicit state duration modeling in the HMM has been developed but it is not sufficient for modeling the intrinsically dynamic, or nonstationary, transition process. Nevertheless, most research efforts have been concerned with only within-state nonstationarity, e.g., variable state duration and regional symbol correlation. In this paper we explore the nonstationarity of Markov chains and propose a nonstationary HMM that is defined with a set of dynamic transition probability parameters A( τ) = { a ij ( τ)}, a function of time duration τ. The model, when compared to the traditional models, is defined as a generalization of the standard HMM and the state duration HMM, with the description being given for discrete observation distributions. Through a set of experiments, it has been shown that the proposed model is more capable of capturing the dynamic nature of signals with higher discrimination power in on-line character recognition.